The quality factor (Q) of a mechanical resonator is defined as the energy stored in the resonator divided by the energy dissipated per vibration cycle. This means the lower the energy loss, the higher the quality factor. Various loss mechanisms will contribute to energy dissipation within a thin-film bulk acoustic resonator, including anchor loss, surface loss, air damping and thermoplastic damping. For a thin-film piezoelectric-on-substrate (TPoS) resonator, the loss mechanisms can be from the surface loss associated with the electrode and the piezoelectric layers, the energy dissipated from the resonator to the supporting substrate, and the air damping loss when the device is operated in air.
Anchor loss or support damping is one of the significant energy loss mechanisms. While the resonator vibrates, the harmonic load excites acoustic waves propagating in support beams, which anchor the resonator to its surrounding substrate, and part of the vibration energy is dissipated through elastic wave propagation into the surrounding substrate. One technique to reduce this “anchor” loss includes placing support beams at nodal points where minimum vibration or displacement is present. An example of this technique is disclosed in article by R. Abdolvand et al., entitled “A Low-Voltage Temperature-Stable Micromechanical Piezoelectric Oscillator,” Proceedings of the 14th International Conference on Solid-State Sensors, Actuators and Microsystems, Lyon, France, Jun. 10-14 (2007), pp. 53-56. Another technique for reducing “anchor” loss, which includes using perforated resonator body supports, is disclosed in commonly assigned U.S. application Ser. No. 12/508,257, filed Jul. 23, 2009, entitled “Thin-Film Bulk Acoustic Resonators Having Perforated Resonator Body Supports That Enhance Quality Factor,” the disclosure of which is hereby incorporated herein by reference.